There are two classical papers
(Matsuda, Sato and Takeda,
1971;
Harrison, 1973)
in which magnetic fields were considered to be
generated by turbulence in the radiation dominated universe. There is
also a close relation between vorticity and magnetic fields,
= - (mc/e) (where
is the vorticity) which
was deduced by
Batchelor (1950)
and considered again by
Kulsrud et al. (1997)
as an extension of a
previous study by Biermann. The deduction is based on the surprising
similarity between the vorticity and the induction equations.
With similar initial conditions, both magnitudes, vorticity and
magnetic fields, should evolve similarly. Viscosity has a
different behaviour, because there is a saturation of vorticity, but
the above equation could be used in other astrophysical problems. In the
epoch of radiation domination, however, we will present arguments
against this, so that this equation probably does not hold.